1. StoryTime StoryTime Nikola Tesla, one of the inventors of radio Nikola Tesla, one of the inventors of radio & an archetypical mad scientist, told a & an archetypical mad scientist, told a reporter the following story about an application of resonance. He built an electric vibrator that fit in his pocket, & attached it to one of the steel beams of a building that was under construction in New York. Although the article didn’t say so, he presumably claimed to have tuned it to the resonant frequency of the building. “ In a few minutes, I could feel the beam trembling. Gradually the trembling increased in intensity and extended throughout the whole great mass of steel. Finally, the structure began to creak & weave, & the steelworkers came to the ground panic-stricken, believing that there had been an earthquake.... [If] I had kept on ten minutes more, I could have laid that building flat in the street.” Is this physically plausible?

2. Open-end Air Columns An open air column has a fundamental frequency of 200 Hz. What is the frequency of the second harmonic (first overtone)? A. 300 Hz B. 400 Hz C. 600 Hz D. 800 Hz If the length of the air column is increased, the frequency of the fundamental is: A. increasedB. decreasedC. the same

3. Open-end Air Columns An open air column has a fundamental frequency of 200 Hz. What is the frequency of the second harmonic (first overtone)? A. 300 Hz B. 400 Hz C. 600 Hz D. 800 Hz If the length of the air column is increased, the frequency of the fundamental is: A. increasedB. decreasedC. the same

4. Resonance in Closed Air Columns 3U Physics

5. Resonance in Closed-End Air Columns If one end of an air column is closed off, it must have a node at that end. The first harmonic of a closed-end air column is therefore:

6. Resonance in Closed-End Air Columns If one end of an air column is closed off, it must have a node at that end. The first harmonic of a closed-end air column is therefore:

7. Resonance in Closed-End Air Columns If one end of an air column is closed off, it must have a node at that end. The first harmonic of a closed-end air column is therefore: Note that = 4L (or L = /4).

8. Higher Harmonics The next higher harmonic that can be produced is:

9. Higher Harmonics The next higher harmonic that can be produced is:

10. Higher Harmonics The next higher harmonic that can be produced is: = 4L/3 or L = 3 /4 = 4L/3 or L = 3 /4

11. Higher Harmonics The next higher harmonic that can be produced is: = 4L/3 or L = 3 /4 = 4L/3 or L = 3 /4 This harmonic is called the 3 rd (and not the 2 nd ) harmonic because its frequency is 3 times that of the fundamental frequency.

12. Higher Harmonics Similarly, the next higher harmonic is the fifth harmonic: = 4L/5 or L = 5 /4 = 4L/5 or L = 5 /4

13. Longitudinal Waves What do these standing waves actually look like?

14. Longitudinal Waves What do these standing waves actually look like?

15. Closed-End Air Columns Example A closed-end air tube resonates to a tuning fork of 480 Hz at lengths of 53.0 cm and 88.5 cm. What is the speed of sound in air?

16. Closed-End Air Column Example A closed-end air tube resonates to a tuning fork of 480 Hz at lengths of 53.0 cm and 88.5 cm. What is the speed of sound in air?

17. Closed-End Air Column Example A closed-end air tube resonates to a tuning fork of 480 Hz at lengths of 53.0 cm and 88.5 cm. What is the speed of sound in air? The difference between one harmonic and the next is a half- wavelength (for open or closed- ends).

18. Closed-End Air Columns Example A closed-end air tube resonates to a tuning fork of 480 Hz at lengths of 53.0 cm and 88.5 cm. What is the speed of sound in air?

19. More Practice Lab: Closed Air Columns and the Speed of Sound